Consider the following from this paper "Correspondences, Motifs and Monoidal Transformations" of Manin [here][1].

> **Theorem.** *Nonsingular three-dimensional projective unirational varieties $V$ over a finite field satisfy the Riemann-Weil hypothesis.*

> **Sketch of the Proof.** We consider a rational map $f: \mathbb{P}^3 \to V$ of finite degree. By virtue of Abhyankar's results there exists a commutative diagram of the form

> [![enter image description here][2]][2]

> in which $g$ is a birational morphism which splits into a sequence of monoidal transformations with nonsingular centers, and $h$ is a morphism of finite degree (at a generic point).

**Question.** What are Abhyankar's results here, and could anybody give a sketch of a proof of them?

  [1]: http://iopscience.iop.org/article/10.1070/SM1968v006n04ABEH001070/pdf
  [2]: https://i.sstatic.net/QppkK.png